Rui Zhang

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In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems proved in [1] for branching OU processes with binary branching mechanisms. Compared with the results of [1], our central(More)
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We consider the problem of estimating a discrete signal X n = (X 1 ,. .. , Xn) based on its noise-corrupted observation signal Z n = (Z 1 ,. .. , Zn). The noise-free, noisy, and reconstruction signals are all assumed to have components taking values in the same finite M-ary alphabet {0,. .. , M − 1}. For concreteness we focus on the additive noise channel Z(More)
Let X = {Xt, t ≥ 0; Pμ} be a critical superprocess starting from a finite measure μ. Under some conditions, we first prove that limt→∞ tPμ(Xt = 0) = ν −1 φ0, μ, where φ0 is the eigenfunction corresponding to the first eigenvalue of the infini-tesimal generator L of the mean semigroup of X, and ν is a positive constant. Then we show that, for a large class(More)
In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and unifies all the central limit theorems obtained recently in [27] for supercritical(More)
Consider a supercritical superprocess X = {X t , t 0} on a locally compact separable metric space (E, m). Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching mechanism is of the form ψ(x, λ) = −a(x)λ + b(x)λ 2 + (e −λy − 1 + λy)n(x, dy), x ∈ E, λ > 0, where a ∈ B b (E), b ∈ B + b (E), and n is a kernel(More)
In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. In the particular case when the state E is a finite set and the underline motion is an irreducible Markov chain on E, our results are superprocess(More)